The man was hit on Friday at least once by gunfire and taken to the hospital still conscious, USA Today reported.
A video of the incident shows the officer shouting at the man to "get down" and firing his weapon at least nine times.
Randall Blankenbaker, assistant Dallas chief of police, told reporters the officer came to the aid of a woman whose car was being smashed by the suspect wielding a rock. Blankenbaker described the suspect as the father of the woman's children.
He said the officer, who was assigned to the airport, was "rushed by the gentleman with the rock." When the suspect refused orders to back off, the officer opened fire.
Ray Williams, who witnessed the attack, also said the man went after the officer with the rock after being asked to stop. At least one video of the incident captured the suspect shouting at the officer to "shoot me, shoot me!"
Blankenbaker said some passengers waiting to go through the security checkpoint were so startled by the gunfire that they rushed through the line. That prompted airport authorities to require all passengers be rescreened. He said the airport was not shut down during the incident.
Dallas Love Field, the smaller of the two major airports in the Dallas area, is located in the northwest portion of the city.